# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0321
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0321?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 287, page id 1041163592:0321
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=321
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000321.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.93
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

PRINCIPLA MATHEMATICA.
Descensus primus
ascensus ultimus
4
22 2
8
Numerus Oscillat. 374 272 7622
26 32 64
12 24 48
833 423 223
Postea Olobum plumbeum, diametro digicorum 2, et pondere
unciarum Romanarum 267. suspendi silo codem, sic uE inter cen-
trum Globi ee punctum suspensionis incervallum esset pedum 1023
ex numerabam oscillationes quibus data mocus pars amitteretur.
labularum sublequentium prior extribet numerum occillacionum.
quibus pars octara motus torius celtarie; secunda numerum oscil.
lationum quibus ejusdem pars quarca amissa Fuie.
Descensus primus
Ascensus ultimus
4 8 16 32 64
32
7 14 28 56
Numerus Oscillat. 226 228 193 140. 90: 53 30
Descensus primus
Ascensus ultimus
4
2
12
4 8 26 32 64
3
6 12 24 48
Numerus Oscillat. 510 518 420 318 204 121 70
In Tabula priore Celigendo ex obserrationibus certiam, quintam
ec septimam, e exponendo relocitates maximas in his observa-
cionibus particulatim per numeros 1, 4. 16 respectire, et genera-
diter per quantitatem V ut supra: emerset in oblerratione tertia
293 A + B + C, in quinta
502 =4 A + 8B + 16C, in seprima
30 = 26 A + 6+ B + 256C. FIxe vero sequationes reductae dane
A = 0, 00r414, B = 0,000297, C=0,000879. Et inde prodie res-
Aencia GElobi cum velocitate V mori, in ca racione ad pondus tuum
unciarum 264, quam habet 0,0009V +0,000207V3 f0,000659V.
ad penduli lonsitudinem 121 digitorum. FF s spectemus cam (0-
lummodo relstentix parrem quae eA in duplicata ratione relocitatis,
haec erit ad pondus Globi ut 0,000659 V. 2d 12r digitos. Prat au-
cem lxec pars resictentia in experimento primo ad pondus Cilobi
lignei unciarum 5722, Ut 0, 002227V. ad 12T: ec inde sic relctentia
Clobi lignei ad relstentiam Clobiplumbei (paribus eorum relocica-
tibus) uc 5722 in 0,002227 2d 26+ in 0,000659, id cA, ut 73 2d 1.
Diametri Giloborum duorum crane 63 ec 2 digitorum, sc harum
quadrata sunc ad invicem ut 47 2 dc 4 seu 1228 e F quamproxime.
Ergo resistentia Globorum aequirelocium erane in minore ratione
quam duplicata diametrorum. Ac nondum considerarimus reli
Aenriam
87
SPCVNDVO